I support the death penalty in only a few cases: Wartime/time-of-conflict treason, crimes against humanity, prison escape/attempted escape while serving a LWOP sentence, and military crimes.
Because this bombing is time-of-conflict treason in my eyes (I actually couldn't dig up the full list of charges they nailed him for, but treason ought to be among them), I advocate the death penalty in this rare case. But Octavious has a good point about the terrible application of the death penalty in the US.
I say give him one good, solid, fair appeal, then execute him by some reliable, inexpensive, reasonably humane, and time-tested method (hanging, firing squad, whatever). No death penalty (except for the proposed but untested nitrogen asphyxiation method) is going to be completely painless, whether it's the poke of a needle or the jerk of a rope. We might as well make it quick. Even the sickest criminals deserve a quick end.